Correlation
Publications pertaining to the correlation of the public and private markets have used the traditional method of computing correlation: plotting a series of index values RM (e.g., the return to the S&P 500 index, the Wilshire 5000 index, the NASDAQ composite, etc.) on the x axis and corresponding stock or portfolio values RS on the y axis, with each pair representing returns for the same time period (daily, monthly, quarterly, annual, etc.). Least squares linear regression of these time series value pairs results in a so-called characteristic line in the form:Rs=αs+βSRm+es
The β parameter of the characteristic line, when multiplied by the market return, describes the systematic return of the stock or portfolio. Put another way, the β parameter describes the relative riskiness of the investment, as defined by periodic volatility in the value of the stock or portfolio relative to the overall market. The e, parameter describes the unsystematic return, i.e., the company-specific or portfolio-specific risk of the stock or portfolio. The α parameter is the y-intercept of the characteristic line, a constant that expresses the stock or portfolio return associated with a market return of zero (the return expected if the market does not change).
Beta, the slope of the characteristic line, can also be described in terms of the covariance of the stock and the market:
      β    s    =                    COV        sm                    σ        m        2              =                            σ          s                ⁢                  σ          m                ⁢                  r          sm                            σ        m        2            
Solving for the correlation coefficient of the stock or portfolio, which is a measure of the percentage of movement in the stock or portfolio associated with the movement in the market, we obtain:
      r    sm    =                    β        s            ⁢              σ        m        2                            σ        s            ⁢              σ        m            
When applied to stocks or portfolios of listed securities in the public markets, this method of estimating correlation works well. When applied to the private markets, however, this method is inherently biased and inaccurate because the interim value of a private market investment or portfolio (i.e., its value prior to realization) is, by its very nature as an illiquid asset, primarily an appraisal or estimate of value. Much as in the real estate market, values are sticky and thus appear to be less volatile (and therefore less risky) than they might be if an active market established values daily. Portfolio values in the private market are also affected by the j-curve phenomenon, in which fees charged against constant portfolio values result in early negative returns. Whether due to sticky values or the j-curve, the end result is an inaccurate determination of correlation.
For example, several correlation matrices, which include buyouts and venture capital, as well as publicly traded stocks and bonds, are published annually in the Venture Economics Yearbook series. The 2000 Yearbook, which covers private equity through Dec. 31, 1999, contains the following data, reported in FIGS. 9.19 and 9.20.
TABLE 1Correlation Based on Quarterly Returns for Longest Individual Series*LargeSmallCorp.T-T-VentureBuyoutsMezzanineEquityStockStockBondsBillsBondsPVCIVenture100.0%8.9%13.7%82.9%39.0%48.7%−18.5%−20.2%−19.2%47.8%Buyouts100.0%21.9%60.1%13.5%9.7%−5.7%−2.7%−10.0%−7.3%Mezzanine100.0%27.3%11.9%21.6%−29.0%−22.4%−32.6%5.6%Equity100.0%40.8%46.5%−20.3%−21.3%−22.9%32.2%Large Stock100.0%77.7%6.8%1.3%2.6%56.6%Small Stock100.0%−4.3%−19.6%−10.1%46.2%Corp. Bonds100.0%9.7%97.5%23.8%T-Bills100.0%7.5%−11.5%T-Bonds100.0%17.2%PVCI100.0%Beta0.800.840.930.431.000.500.27—0.380.73*Venture Economics 2000 Yearbook, FIG. 9.19
TABLE 2Correlation Based on Annual Returns for Longest Series in Common**LargeSmallCorp.T-T-VentureBuyoutsMezzanineEquityStockStockBondsBillsBondsPVCIVenture100.0%−0.9%−14.4%89.1%22.3%39.7%−42.4%−33.5%−38.0%69.8%Buyouts100.0%42.6%38.1%20.4%28.7%8.4%−8.3%10.3%−11.0%Mezzanine100.0%6.7%0.8%8.0%32.8%−9.3%39.2%−13.0%Equity100.0%27.4%50.9%−42.4%−48.4%−36.1%60.4%Large Stock100.0%62.6%54.9%6.1%56.7%53.6%Small Stock100.0%30.9%−34.2%30.4%57.7%Corp. Bonds100.0%40.8%98.6%5.7%T-Bills100.0%32.8%32.8%T-Bonds100.0%4.2%PVCI100.0%Beta0.910.820.930.711.000.550.32—0.410.78**(Venture Economics 2000 Yearbook, FIG. 9.20
These two correlation matrices were calculated using the time-weighted rates of return of the securities they contain. They probably understate the correlation of the private markets and the public markets (and of the private markets to each other), as discussed above, because private market valuations stay relatively constant over fairly long periods of time (e.g., most private equity firms hold investments owned less than one year at cost, which is a constant) or decline (because of the j-curve phenomenon), while the market's values rise and fall daily. As a result, correlations looked at over the short run appear to be low—over short time periods the private investment value does not move much in sympathy with the public market, the independent variable—which is why, in the correlation matrices shown above, correlations are much higher over yearly periods (Table 2) than they are over quarterly periods (Table 1).
The best way to remedy these deficiencies of the conventional correlation computation would be to match private market and public market investment outcomes over the same or very similar periods of time, in order to allow the movement of private market values to be realized and thus known with certainty. Realized values are not sticky valuations or biased estimates. They are cash or liquid securities, and thus outcomes that are directly comparable to the liquid alternatives available in an index of listed securities.
Benchmark
The present inventors previously published the Index Comparison Method (“ICM”) and developed it into a performance diagnostic. Since its publication, the ICM has been adopted by many of the largest and most sophisticated U.S. and European institutional investors and major consulting firms. The ICM also appears in the Venture Economics annual survey as the BLNC measure (the LN is for Long-Nickels) (2000 Investment Benchmarks Report, Venture, Capital, Venture Economics, Jesse Reyes, Editor in Chief, FIGS. 9.21, 9.22, 9.23 and 9.24).
The ICM is calculated, in simple terms, by the following steps:    1. Compute the internal rate of return of the private investment portfolio,            Obtain private investment asset, vintage and/or overall portfolio actual returns by listing their cash flows in columns, each cash flow accompanied by its date, using natural signs (i.e. cash inflows are positive numbers and cash outflows are negative numbers).        The final cash flow for each investment is its value at the report date (i.e. all valuations are assumed realized at the report date unless they have in fact been realized at an earlier date).        Compute an IRR for the private investment asset, vintage and/or overall portfolios using these cash flows.            2. Compute the comparable total return to an index of public stocks had the cash flows in 1. been invested in the index.            List all cash flows as above for actual portfolio returns, but without showing an ending value/cash flow.        Compute the ending value/cash flow as follows:                    (a) Treat the first (negative) cash flow as having been invested in the relevant index.            (b) Using an end-of-period assumption, grow that cash flow over the time between the first and second cash flow at the rates indicated by the linked index.            (c) At the point of the next cash flow, grow the new net amount (i.e. the amount of the prior cash flow grown by the linked index return plus the new cash flow) by the relevant linked index until the date of the next cash flow.            Note that the next cash flow could be a distribution from the private investment, which would be treated as a withdrawal from the index investment. Thus the new net amount could be the amount of the prior cash flow grown by the linked index return minus the new cash flow.            (d) Repeat step (c) until the calculation arrives at the current report date.            (e) Compute the IRR of the investment using the portfolio value at the current report date, as computed in steps (a)-(d), as the final cash flow/valuation as in the actual portfolio return computation above.The result is a dollar-weighted time-weighted rate of return to the public index that is directly comparable to the IRR performance of the private investment.                        
The return to the public index represents the opportunity cost of investing in the private markets. This opportunity cost concept can be viewed as a benchmark: if the opportunity cost is a positive number (i.e., RM−RS≧0), the private investment underperformed the public market; if opportunity cost is a negative number (i.e., RM−RS≦0)m the private investment outperformed the public market.